Goal

from a selection of possible subset/chosen ESMs, come up with a metric for each of thoes subsets that says how good the subset is at representing the ‘truth’ that is the PCA of all of the CMIP6 data.

Then select the subset of ESMs with the smallest value for that metric and those are our ‘curated archive’ ESMs.

Work below covers 2 different metrics:

The projection of all CMIP6 data into the first N eigenvectors from the PCA of all data vs projection of all CMIP6 data into the first N eigenvectors from the PCA of the subset data. Calculate NRMS between those two projections for each CMIP6 esmXscenario. Metric is the average value of all of those NRMS’s.

saying for each subset of 5 ESMs, how similar is all CMIP6 data projected into that subset’s space vs projected into the ‘true’ space

The coefficients of all CMIP6 data into the first N eigenvectors from the PCA of all data. For each of the OOS esmXscenarios, for each subset ESM, calculate the smallest L2 distance from the coefficients across the subset ESM’s scenarios= how close each subset ESM can get to every out of sample data point. Then take the minimum across subset ESMs = how close the selected subset can get to each OOS data point. The average of that distance from all OOS data points is then the metric for that subset.

could weight by amount of variance explained by each dimension.

set up

And some package and labeling info

library(ggplot2)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(tidyr)


timeseries_dir <- 'extracted_timeseries/'

metrics_write_dir <-  'extracted_timeseries/extracted_metrics/'


# strawman subset of ESMs from our original 12, have all 4 experiments each
subset <- c('CAMS-CSM1-0' , 'FGOALS-g3', 'MRI-ESM2-0' ,'CESM2-WACCM', 'CanESM5')
subset2 <- c('CAMS-CSM1-0' , 'FGOALS-g3', 'MRI-ESM2-0' ,'CESM2-WACCM', 'UKESM1-0-LL')
            

# ESMS that dont have 4 experiments
non_candidate_esm <- c("CIESM", "E3SM-1-1", "FIO-ESM-2-0", "GFDL-CM4", "IITM-ESM",
                       "IPSL-CM5A2-INCA", "KIOST-ESM", "NESM3", "NorESM2-LM")

Load ESM data that’s been processed

region_summary_main <- read.csv(paste0(metrics_write_dir, 'IPCC_land_regions_metrics.csv'), 
                                stringsAsFactors = FALSE)
region_summary_main %>%
  filter(experiment != 'ssp119',
         experiment != 'ssp434',
         experiment != 'ssp460',
         experiment != 'ssp534-over')  %>%
    rename(region = acronym) ->
  region_summary 

print(head(region_summary))

##          esm experiment ensemble variable       type              name region
## 1 ACCESS-CM2     ssp126 r1i1p1f1       pr       Land Arabian-Peninsula    ARP
## 2 ACCESS-CM2     ssp126 r1i1p1f1       pr       Land    Central-Africa    CAF
## 3 ACCESS-CM2     ssp126 r1i1p1f1       pr Land-Ocean         Caribbean    CAR
## 4 ACCESS-CM2     ssp126 r1i1p1f1       pr       Land       C.Australia    CAU
## 5 ACCESS-CM2     ssp126 r1i1p1f1       pr       Land   C.North-America    CNA
## 6 ACCESS-CM2     ssp126 r1i1p1f1       pr       Land            E.Asia    EAS
##           iasd      end_val   end_anomaly end_anomaly_pct mid_century_val
## 1 7.227917e-07 1.700625e-06  4.306991e-07     0.339153029    2.051770e-06
## 2 3.009324e-06 4.828026e-05 -4.965491e-08    -0.001027416    4.941042e-05
## 3 6.106140e-06 3.052769e-05  2.089845e-07     0.006892922    3.429079e-05
## 4 2.830779e-06 1.130480e-05 -1.269868e-06    -0.100986213    1.126320e-05
## 5 2.861294e-06 3.232150e-05  1.953880e-06     0.064340892    3.222543e-05
## 6 2.687448e-06 5.449186e-05  5.826705e-06     0.119730531    5.260652e-05
##     mid_anomaly mid_anomaly_pct
## 1  7.818446e-07      0.61566180
## 2  1.080502e-06      0.02235680
## 3  3.972086e-06      0.13101110
## 4 -1.311461e-06     -0.10429388
## 5  1.857811e-06      0.06117738
## 6  3.941364e-06      0.08098944

Prep data for PCA

# reshape:
grouped_data <- split(region_summary, list(region_summary$esm, region_summary$experiment))
grouped_data <- grouped_data[sapply(grouped_data, function(x) dim(x)[1]) > 0]

shaped_data <- lapply(grouped_data, function(group){
    if (nrow(group) >0) {
      group %>%
        filter(variable == 'tas') %>% 
        select(esm, experiment, ensemble,type, region,
               iasd, end_anomaly, mid_anomaly) %>%
        rename(tas_iasd = iasd,
               tas_end_anomaly = end_anomaly,     
               tas_mid_anomaly = mid_anomaly) %>% 
        left_join(group %>%
                      filter(variable == 'pr') %>% 
                      select(esm, experiment, ensemble,type, region,
                             iasd, end_anomaly_pct, mid_anomaly_pct) %>%
                      rename(pr_iasd = iasd,
                             pr_end_anomaly_pct = end_anomaly_pct,    
                             pr_mid_anomaly_pct = mid_anomaly_pct),
                  by = c('esm','experiment', 'ensemble', 'type', 'region')
               ) ->
    reshaped
    
    reshaped %>%
        group_by(esm, experiment, type, region) %>%
        summarize(tas_iasd=mean(tas_iasd),
                  tas_end_anomaly=mean(tas_end_anomaly, na.rm = T),
                  tas_mid_anomaly = mean(tas_mid_anomaly, na.rm = T),
                  pr_iasd = mean(pr_iasd, na.rm = T),
                  pr_end_anomaly_pct = mean(pr_end_anomaly_pct, na.rm = T),
                  pr_mid_anomaly_pct = mean(pr_mid_anomaly_pct, na.rm = T) ) %>%
        ungroup() %>%
        mutate(ensemble = 'ensemble_avg') -> #%>%
        #bind_rows(reshaped) ->
        reshaped2
    
    #TODO need to change shaping if including ensemble members
    reshaped2 %>%
        select(-type) %>%
        gather(metric, value, -esm, -experiment, -ensemble, -region) %>%
        mutate(row_id = paste0(region, '~', metric),
           col_id = paste0(esm, '~', experiment, '~', ensemble)) %>%
        select(-esm, -experiment,-ensemble, -region, -metric) %>%
        as.data.frame() ->
    reshaped3 
  
  colnames(reshaped3) <- c(paste0(unique(reshaped3$col_id)), 'row_id', 'col_id')
  rownames(reshaped3) <- paste0(reshaped3$row_id)
  
  reshaped3 %>% 
    select(-col_id, -row_id) ->
    out
  
  return(out)  
    }
    
    }
)

# combine columns but then transpose because prcomp wants rows to be observations 
# and columns to be variables (but doing it the other way first is easier to code)
full_data <- t(do.call(cbind, shaped_data) )


# Drop anything with missing data
full_data1 <- na.omit(full_data)
print('removed rows due to missing data')

## [1] "removed rows due to missing data"

print(row.names(full_data)[c(which(!(row.names(full_data) %in% row.names(full_data1))))])

## [1] "CIESM~ssp126~ensemble_avg"      "CIESM~ssp245~ensemble_avg"     
## [3] "CIESM~ssp585~ensemble_avg"      "NorESM2-LM~ssp585~ensemble_avg"

full_data <- as.data.frame(full_data1)
rm(full_data1)

And the subsetted ESMs

as.data.frame(full_data) %>%
    mutate(temp = row.names(.)) %>%
    separate(temp, into=c('esm', 'trash'), sep = '~', extra='merge') %>%
    filter(esm %in% subset) %>% 
    select(-esm, -trash) %>%
    as.matrix(.) ->
    subdata

PCA

cmip6 ‘truth’

full_pca <- prcomp(full_data, center=TRUE, scale = TRUE)


# eigenspace from the PCA
full_eigenval <- data.frame(eigenvalues=(full_pca$sdev)^2)
full_eigenvec <- full_pca$rotation

# skree
var_explained_df <- data.frame(var_explained=(full_pca$sdev)^2/sum((full_pca$sdev)^2)) %>%
    mutate(PC = as.integer(row.names(.)))

var_explained_df %>%
  ggplot(aes(x=PC,y=var_explained, group=1))+
  geom_point(size=4)+
  geom_line()+
  labs(title="Scree plot: PCA on scaled data - all ESMs")

pfull <- var_explained_df %>%
    filter(PC <=15)%>%
  ggplot(aes(x=PC,y=var_explained, group=1))+
  geom_point(size=4)+
  geom_line()+
  labs(title="Scree plot: PCA on scaled data - all ESMs")

pfull

subset

Functionalise from here, basically I think? :

sub_pca <- prcomp(subdata, center=TRUE, scale = TRUE)


# eigenspace from the PCA
sub_eigenval <- data.frame(eigenvalues=(sub_pca$sdev)^2)
sub_eigenvec <- sub_pca$rotation

# skree
var_explained_dfsub <- data.frame(var_explained=(sub_pca$sdev)^2/sum((sub_pca$sdev)^2)) %>%
    mutate(PC = as.integer(row.names(.)))

var_explained_dfsub %>%
  ggplot(aes(x=PC,y=var_explained, group=1))+
  geom_point(size=4)+
  geom_line()+
  labs(title="Scree plot: PCA on scaled data - subset ESMs")

psub<- var_explained_dfsub %>%
    filter(PC <=15)%>%
  ggplot(aes(x=PC,y=var_explained, group=1))+
  geom_point(size=4)+
  geom_line()+
  labs(title="Scree plot: PCA on scaled data - subset ESMs")
psub

side by side scree

pfull

psub

-> first five eigenvalues focus

Compare subset PCA space with full PCA space

differences in the projections of the same data

We’ve picked our subset of ESMs, so we project each available CMIP6 data row into:

the first 5 eigenvectors of the full data
the first 5 eigenvectors of the subset data

Then compare those projections.

then this will be repeated for every combination of 5 ESMs

Then pick the combo of 5 ESMs based on minimizing error for all observations.

Pro: don’t have to set a cutoff, can just select subset with smallest error
con: a lot of calculations

# project new data onto the PCA space
#TODO double check with fresher eyes
project_pca <- function(data, pca, n_eigenvalues=5){
    
    # don't need this for full data on full pca, could just do pca$x[,1:n]
    # but for full data on sub pca, do need this:
    coeff <- scale(data, pca$center, pca$scale) %*% pca$rotation[,1:n_eigenvalues]
    
    reconstructions <- sapply(1:nrow(data), function(rowindex){
        reconstructed <- rowSums(sweep(pca$rotation[,1:n_eigenvalues], 
                                       MARGIN=2,
                                       coeff[rowindex,],
                                       `*`))
        return(reconstructed)
    })
    
    colnames(reconstructions) <- rownames(data)
    return(reconstructions)
}

# reconstruct the subdata in the space of first 5 eigenvectors of full data
recon_full <- project_pca(data = full_data, pca = full_pca, n_eigenvalues = 5)


# reconstruct the subdata in the space of first 5 eigenvectors of sub data
recon_sub <- project_pca(data = full_data, pca = sub_pca, n_eigenvalues = 5)

errs <- data.frame()
for (colindex in 1:ncol(recon_sub)){

    sub <- recon_sub[, colindex]
    full <- recon_full[,colindex]
    
    bind_rows(data.frame(id = colnames(recon_sub)[colindex]) %>%
                  mutate(rms = sqrt(sum((sub - full)^2)) ,
                         nrms = rms /sqrt(sum((full)^2))) ,
              errs) ->
        errs

}


errs %>%
    separate(id, into = c('esm', 'scenario', 'ensemble'), sep ='~')  %>%
    group_by(esm) %>%
    summarize(avg_nrms_across_exps = mean(nrms)) %>%
    ungroup ->
    nrms

mean(nrms$avg_nrms_across_exps)

## [1] 0.558996

compare coefficients in full PCA space

from the set of available coefficients in the full PCA space, select models whose coefficients span the space in the sense of:

every ESM is ‘close enough’ to one of the selected models in terms of L2 distance of coefficients
Pro: only need the full pca, not a pca of every candidate subset so fewer calculations
Con: have to decide on a cutoff

n_eigenvalues <- 5


coeff <- as.data.frame(full_pca$x[,1:n_eigenvalues])

# reshape so have info by ESM and experiment
coeff %>%
    mutate(id = row.names(.)) %>%
    separate(id, into = c('esm', 'scenario', 'ensemble'), sep ='~') %>%
    gather(pc, value, -esm, -scenario, -ensemble) -> # %>%
    # spread(scenario, value) ->
    coeff_all_ESM


# pull off the subset coefficients into their own DF for comparison
coeff_all_ESM %>%
    filter(esm %in% subset)  %>%
    spread(scenario, value) ->
    coeff_sub_ESM

out <- data.frame()
for (esmname in unique(coeff_all_ESM$esm)){
    
    if(!(esmname %in% subset)){
        
        coeff_all_ESM %>%
            filter(esm == esmname) ->
            oos 
        
        
        # For each subset ESM, compare each oos scenario with all 4 scenarios
        # and record the smallest. Then have a data frame with how close each
        # subset ESM can get to each scenario of the oos ESM.
        oos %>%
            left_join(coeff_sub_ESM %>%    
                          select(-ensemble) %>%
                          rename(subset_ESM = esm), 
                      by = 'pc') %>%
            group_by(esm, scenario, ensemble, subset_ESM) %>%
            summarise(closest_L2 = min( sqrt(sum((value-ssp126)^2)),
                                     sqrt(sum((value-ssp245)^2)),
                                     sqrt(sum((value-ssp370)^2)),
                                     sqrt(sum((value-ssp585)^2))))  %>%
            ungroup %>% 
            # Then fillter to just the closest on each scenario
            group_by(esm, scenario, ensemble) %>%
            filter(closest_L2 == min(closest_L2)) %>%
            ungroup %>%
            bind_rows(out, .) ->
            out
        
        # If there is only one subset ESM that's closest for each scenario,
        # obviously just pick that. But not sure where to go from there.

    }
}

# take average L2 for all oos esms - that's the characteristic value for this
# particular subset. Then pick the subset that has smallest characteristic value.

mean(out$closest_L2)

## [1] 6.611159

may be the case that from a stitches perspective, we want to block compare ESM to ESM (so concatenate experiments into super vector of coeff) but how to handle ESMs that don’t have all the experiments for that comparison? if ACCESS is the oos ESM and didn’t do ssp245, we’d need to like find the ESM with the 3 most similar experiments, not necessarily just exclude 245 from the chosen
but also even oos ESM has all 4 experiments, why should we necessarily care about 245 being close to 245. Maybe 126 and 245 are close to 245 and that’s fine.
^ That’s what I’m doing but Can convince myself either way - one oos ESM-Exp combo being similar to one chosen ESM-Exp combo is enough for stitches to cover all behaviors; OR really need ESM to ESM comparison only

ESM selection

Then we would be brute force looping over eligible combinations of 5 ESMs (have all 4 scenarios, maybe some criteria on number ensemble members, and represent ECS distribution) and pick the one with either smallest vector differences = the axes are closest or the smallest projection differences.

Con of either method: not suitable for in-filling if decide to add an extra ESM but could probably be adapted? Like maybe we chose 5 so we want to see what the best ESM to add as 6 conditional on the 5 we already have would be? which may be different than the 6 best
30 ESMs in list total, 8 have a missing experiment
22 choose 5 = 26334 combinations (better than 30 choose 5, 142k)
we should aim to whittle down either on the front end by less than 22 - require some amount of ensemble members and/or represent ECS

functionalized

get_subset_data <- function(esmsubset, fulldata){
    as.data.frame(fulldata) %>%
        mutate(temp = row.names(.)) %>%
        separate(temp, into=c('esm', 'trash'), sep = '~', extra='merge') %>%
        filter(esm %in% esmsubset) %>% 
        select(-esm, -trash) %>%
        as.matrix(.) ->
        subdata
    
    return(subdata)
}


project_pca <- function(data, pca, n_eigenvalues=5){
    
    # don't need this for full data on full pca, could just do pca$x[,1:n]
    # but for full data on sub pca, do need this:
    coeff <- scale(data, pca$center, pca$scale) %*% pca$rotation[,1:n_eigenvalues]
    
    reconstructions <- sapply(1:nrow(data), function(rowindex){
        reconstructed <- rowSums(sweep(pca$rotation[,1:n_eigenvalues], 
                                       MARGIN=2,
                                       coeff[rowindex,],
                                       `*`))
        return(reconstructed)
    })
    
    colnames(reconstructions) <- rownames(data)
    return(reconstructions)
}


compare_projections <- function(fulldata, fullpca, subpca, n_eigenvalues = 5){
    
    # reconstruct the subdata in the space of first 5 eigenvectors of full data
    recon_full <- project_pca(data = fulldata,
                              pca = fullpca, 
                              n_eigenvalues = n_eigenvalues)
    
    # reconstruct the subdata in the space of first 5 eigenvectors of sub data
    recon_sub <- project_pca(data = fulldata,
                             pca = subpca,
                             n_eigenvalues = n_eigenvalues)
    
    
    # compare reconstructions 
    errs <- data.frame()
    for (colindex in 1:ncol(recon_sub)){
        sub <- recon_sub[, colindex]
        full <- recon_full[,colindex]
        
        bind_rows(data.frame(id = colnames(recon_sub)[colindex]) %>%
                      mutate(rms = sqrt(sum((sub - full)^2)) ,
                             nrms = rms /sqrt(sum((full)^2))) ,
                  errs) ->
            errs
        } 
    
    errs %>%
        separate(id, into = c('esm', 'scenario', 'ensemble'), sep ='~')  %>%
        group_by(esm) %>%
        summarize(avg_nrms_across_exps = mean(nrms)) %>%
        ungroup ->
        nrms
    
    return(data.frame(avg_nrms_across_esms = mean(nrms$avg_nrms_across_exps)))
}

full_pca_distances <- function(subset_esms, fullpca, n_eigenvalues = 5){

    coeff <- as.data.frame(fullpca$x[,1:n_eigenvalues])
    
    # reshape so have info by ESM and experiment
    coeff %>%
        mutate(id = row.names(.)) %>%
        separate(id, into = c('esm', 'scenario', 'ensemble'), sep ='~') %>%
        gather(pc, value, -esm, -scenario, -ensemble) -> # %>%
        # spread(scenario, value) ->
        coeff_all_ESM
    
    # pull off the subset coefficients into their own DF for comparison
    coeff_all_ESM %>%
        filter(esm %in% subset_esms)  %>%
        spread(scenario, value) ->
        coeff_sub_ESM
    
    out <- data.frame()
    for (esmname in unique(coeff_all_ESM$esm)){
        
        # only calculate for oos ESMs
        if(!(esmname %in% subset_esms)){
            
            coeff_all_ESM %>%
                filter(esm == esmname) ->
                oos 
            
            # For each subset ESM, compare each oos scenario with all 4 scenarios
            # and record the smallest. Then have a data frame with how close each
            # subset ESM can get to each scenario of the oos ESM.
            oos %>%
                left_join(coeff_sub_ESM %>%    
                              select(-ensemble) %>%
                              rename(subset_ESM = esm), 
                          by = 'pc') %>%
                group_by(esm, scenario, ensemble, subset_ESM) %>%
                summarise(closest_L2 = min( sqrt(sum((value-ssp126)^2)),
                                            sqrt(sum((value-ssp245)^2)),
                                            sqrt(sum((value-ssp370)^2)),
                                            sqrt(sum((value-ssp585)^2))))  %>%
                ungroup %>% 
                # Then filter to just the closest of any subset ESM
                # on each oos scenario
                group_by(esm, scenario, ensemble) %>%
                filter(closest_L2 == min(closest_L2)) %>%
                ungroup %>%
                bind_rows(out, .) ->
                out
            # If there is only one subset ESM that's closest for each scenario,
            # obviously just pick that. But not sure where to go from there.
            }        # end calculation for each subset esm
        
        } # end loop over all ESMs
    
    # take average L2 for all oos esms - that's the characteristic value for this
    # particular subset. Then pick the subset that has smallest characteristic value.
    
    return(data.frame(avg_closest_L2 = mean(out$closest_L2)))
    
}


########

# test functions
suppressMessages(compare_projections(fulldata = full_data,
                          fullpca = full_pca,
                          subpca = sub_pca,
                          n_eigenvalues = 5))

##   avg_nrms_across_esms
## 1             0.558996

suppressWarnings(suppressMessages(full_pca_distances(subset_esms = subset,
                   fullpca = full_pca,
                   n_eigenvalues = 5)))

##   avg_closest_L2
## 1       6.611159

Test

Would load all the regional metric, reshape, do full PCA still.

Then suppose we have labeled subsets

table_of_subsets <- bind_rows(data.frame(subset_id = rep('subset1', 5),
                                         subset = subset),
                              data.frame(subset_id = rep('subset2', 5),
                                         subset = subset2))
knitr::kable(table_of_subsets)

subset_id	subset
subset1	CAMS-CSM1-0
subset1	FGOALS-g3
subset1	MRI-ESM2-0
subset1	CESM2-WACCM
subset1	CanESM5
subset2	CAMS-CSM1-0
subset2	FGOALS-g3
subset2	MRI-ESM2-0
subset2	CESM2-WACCM
subset2	UKESM1-0-LL

rm(subset)
rm(subset2)
rm(subdata)
rm(sub_pca)

For each subset, calculate the two metrics.

metrics <- data.frame()

for (subsetid in unique(table_of_subsets$subset_id)){
    
    subset <- table_of_subsets[table_of_subsets['subset_id']==subsetid,]$subset

    get_subset_data(esmsubset = subset,
                    fulldata = full_data) ->
        subdata
    
    sub_pca <- prcomp(subdata, center=TRUE, scale = TRUE)
    
    data.frame(subset_id = subsetid,
               projection_metric = compare_projections(fulldata = full_data,
                                                       fullpca = full_pca,
                                                       subpca = sub_pca,
                                                       n_eigenvalues = 5),
               coeff_metric = full_pca_distances(subset_esms = subset,
                                                 fullpca = full_pca,
                                                 n_eigenvalues = 5)) %>%
        bind_rows(metrics, .)->
        metrics
               
    rm(subset)
    rm(subdata)
    rm(sub_pca)
    
}

write.csv(metrics, 'esm_subsets_metrics.csv', row.names = FALSE)

all subsets

nESMs <- 5

region_summary %>%
    select(esm) %>%
    distinct %>% 
    filter(!(esm %in% non_candidate_esm)) ->
    df

as.data.frame(t(apply(combn(nrow(df), nESMs), 
                      2, function(i) df[i,])
                )
              ) %>%
    mutate(subset_id = paste0('subset', as.integer(row.names(.)))) %>%
    gather(trash, subset, -subset_id) %>%
    select(-trash) %>%
    arrange(subset_id) ->
    table_of_subsets
write.csv(table_of_subsets, 'subsets_22choose5.csv', row.names = FALSE)


metrics <- data.frame()
    
for (subsetid in unique(table_of_subsets$subset_id)){
    
    subset <- table_of_subsets[table_of_subsets['subset_id']==subsetid,]$subset

    get_subset_data(esmsubset = subset,
                    fulldata = full_data) ->
        subdata
    
    sub_pca <- prcomp(subdata, center=TRUE, scale = TRUE)
    
    data.frame(subset_id = subsetid,
               projection_metric = suppressMessages(compare_projections(fulldata = full_data,
                                                       fullpca = full_pca,
                                                       subpca = sub_pca,
                                                       n_eigenvalues = 5)),
               coeff_metric = suppressWarnings(suppressMessages(full_pca_distances(subset_esms = subset,
                                                 fullpca = full_pca,
                                                 n_eigenvalues = 5)))) %>%
        bind_rows(metrics, .)->
        metrics
               
    rm(subset)
    rm(subdata)
    rm(sub_pca)
    
}

write.csv(metrics, 'esm_subsets_metrics_22choose5.csv', row.names = FALSE)

Take a look at minimizing sets of ESMs

metrics <- read.csv('esm_subsets_metrics_22choose5.csv') %>%
    rename(projection_metric = avg_nrms_across_esms,
           coefficient_metric = avg_closest_L2)
table_of_subsets <- read.csv('subsets_22choose5.csv')



# Subset that is minimum in the projection metric
metrics %>%
    filter(projection_metric == min(projection_metric)) %>%
    left_join(table_of_subsets, by = c('subset_id')) ->
    projection_min

metrics %>%
    filter(coefficient_metric == min(coefficient_metric)) %>%
    left_join(table_of_subsets, by = c('subset_id')) ->
    coefficient_min

knitr::kable(projection_min)

subset_id	projection_metric	coefficient_metric	subset
subset21172	0.502208	7.527474	CESM2-WACCM
subset21172	0.502208	7.527474	CanESM5
subset21172	0.502208	7.527474	INM-CM4-8
subset21172	0.502208	7.527474	INM-CM5-0
subset21172	0.502208	7.527474	MRI-ESM2-0

knitr::kable(coefficient_min)

subset_id	projection_metric	coefficient_metric	subset
subset11961	0.691582	5.426009	BCC-CSM2-MR
subset11961	0.691582	5.426009	CESM2
subset11961	0.691582	5.426009	CMCC-ESM2
subset11961	0.691582	5.426009	MRI-ESM2-0
subset11961	0.691582	5.426009	UKESM1-0-LL

plotting in full PCA space

full_pca$x %>%
  as.data.frame() %>%
  mutate(id = row.names(.)) %>%
  separate(id, into=c('model', 'scenario', 'ensemble'), sep = '~') %>%
  select(model, scenario, PC1, PC2, PC3, PC4, PC5, PC6, PC7, PC8, PC9)->
  coordinates

PC1 vs PC2

ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario))+
    ggtitle('PCA of full data')

p1 <- ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% projection_min$subset),
               mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, projection metric minimizers')

p2 <- ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% coefficient_min$subset),
               mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, coefficient metric minimizers')

gridExtra::grid.arrange(p1, p2)

PC1 vs PC3

p3 <- ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% projection_min$subset),
               mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, projection metric minimizers')

p4 <- ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% coefficient_min$subset),
               mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, coefficient metric minimizers')

gridExtra::grid.arrange(p3, p4)

notes

So this seems like a spot where some heuristics might be helpful.

Throw out any subsets that have multiple models from the same lineage before pulling minimums
Maybe don’t accept any subsets with MRI
Other heuristics, like ECS, number of ensemble members, variables.

table_of_subsets %>%
    group_by(subset_id) %>%
    mutate(keep = if_else('MRI-ESM2-0' %in% subset, 0, 1)) %>%
    ungroup %>%
    filter(keep == 1) ->
    table_of_subsets2


metrics %>%
    filter(subset_id %in% table_of_subsets2$subset_id) %>%
    filter(projection_metric == min(projection_metric)) %>%
    left_join(table_of_subsets, by = c('subset_id')) ->
    projection_min

metrics %>%
    filter(subset_id %in% table_of_subsets2$subset_id) %>%
    filter(coefficient_metric == min(coefficient_metric)) %>%
    left_join(table_of_subsets, by = c('subset_id')) ->
    coefficient_min

knitr::kable(projection_min)

subset_id	projection_metric	coefficient_metric	subset
subset20648	0.5529522	6.597764	CESM2-WACCM
subset20648	0.5529522	6.597764	CMCC-ESM2
subset20648	0.5529522	6.597764	CanESM5
subset20648	0.5529522	6.597764	INM-CM4-8
subset20648	0.5529522	6.597764	MPI-ESM1-2-LR

knitr::kable(coefficient_min)

subset_id	projection_metric	coefficient_metric	subset
subset11861	0.7248628	5.979316	BCC-CSM2-MR
subset11861	0.7248628	5.979316	CESM2
subset11861	0.7248628	5.979316	CMCC-CM2-SR5
subset11861	0.7248628	5.979316	MIROC6
subset11861	0.7248628	5.979316	UKESM1-0-LL
subset11952	0.7305381	5.979316	BCC-CSM2-MR
subset11952	0.7305381	5.979316	CESM2
subset11952	0.7305381	5.979316	CMCC-ESM2
subset11952	0.7305381	5.979316	MIROC6
subset11952	0.7305381	5.979316	UKESM1-0-LL

PC1 vs PC2

gridExtra::grid.arrange(ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% projection_min$subset),
               mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, projection metric minimizers, exclude MRI'),
p1)

gridExtra::grid.arrange(ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% coefficient_min$subset),
               mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, coefficient metric minimizers, exclude MRI'),
p2)

gridExtra::grid.arrange(ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% projection_min$subset),
               mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, projection metric minimizers, exclude MRI'),
    ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% coefficient_min$subset),
               mapping = aes(x = -PC1, y = PC2, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, coefficient metric minimizers, exclude MRI'))

PC1 vs PC3

gridExtra::grid.arrange(ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% projection_min$subset),
               mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, projection metric minimizers, exclude MRI'),
p3)

gridExtra::grid.arrange(ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% coefficient_min$subset),
               mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, coefficient metric minimizers, exclude MRI'),
p4)

gridExtra::grid.arrange(ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% projection_min$subset),
               mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, projection metric minimizers, exclude MRI'),
    ggplot(coordinates) +
    geom_point(mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario)) +
    geom_point(data = coordinates %>% filter(model %in% coefficient_min$subset),
               mapping = aes(x = -PC1, y = PC3, color = model, shape = scenario),
               size = 4) +
    ggtitle('PCA of full data, coefficient metric minimizers, exclude MRI'))

Validation

Hawkins and Sutton 09/Lehner2020: do for full data, do for final subset of ESMs and compare?

From Lehner https://esd.copernicus.org/articles/11/491/2020/esd-11-491-2020.pdf

T and P globally and regionally over time; and gridded for time slices

the model uncertainty M is calculated as the variance across the ensemble means of the seven SMILEs (i.e., across the forced responses of the SMILEs).
internal variability uncertainty I is calculated as the variance across ensemble members of a given SMILE, yielding one estimate of I per model. Prior to this calculation, time series are smoothed with the running mean corresponding to the target metric (here mostly decadal means). Averaging across the seven I values yields the multimodel mean internal variability uncertainty Imean. Alternatively, to explore the assumption that Imean does not change over time, we use the 1950–2014 average value of Imean throughout the calculation (i.e., Ifixed). We also use the model with the largest and smallest I , i.e., Imax and Imin, to quantify the e influence of model uncertainty in the estimate of I.
Following HS09, we calculate S as the variance across the multimodel means calculated for the different emissions scenarios, using a consistent set of available models.

Then how do I want to apply that to our IPCC regional metrics (ideally) or the full time series

Eigenspaces

acs

Goal

set up

Load ESM data that’s been processed

Prep data for PCA

PCA

cmip6 ‘truth’

subset

side by side scree

Compare subset PCA space with full PCA space

differences in the projections of the same data

compare coefficients in full PCA space

ESM selection

functionalized

Test

all subsets

Take a look at minimizing sets of ESMs

plotting in full PCA space

PC1 vs PC2

PC1 vs PC3

notes

PC1 vs PC2

PC1 vs PC3

Validation